Applies spectral theory of stationary kinetic equations to contemporary models of confined matter dynamics.

Derives original well-balanced schemes involving S-matrices (following early Glimm–Sharp's ideas) for kinetic models like chemotaxis or Vlasov–Fokker–Planck coupled to attractive Poisson equation.

Hybridizes this framework in order to support strongly singular hydrodynamic limits, where kinetic distributions concentrate into Dirac atoms, for which rigorous results are proved.